Remark 1.8 The classification of CB generated big mapping class groups in [1]} was
carried out in a larger class of tame surfaces where only certain
ends are assumed to have stable neighborhoods. Most of the arguments in this paper
still work in the setting of tame surfaces as well, for example, an essential
shift does always imply infinite asymptotic dimension. However, without the
assumption that \(\Sigma \)  is stable, \(E\)  being two sided does not imply
existence of a shift map. Hence the statement and some arguments are cleaner
with this assumption. The class of stable surfaces, first used in
[2]}, is a large and natural class of surfaces to work with and it
includes all easily constructed infinite type surfaces.

